Question: Solve for $x$ and $y$ using elimination. ${5x+y = 40}$ ${4x-y = 14}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the top and bottom equations together. $9x = 54$ $\dfrac{9x}{{9}} = \dfrac{54}{{9}}$ ${x = 6}$ Now that you know ${x = 6}$ , plug it back into $\thinspace {5x+y = 40}\thinspace$ to find $y$ ${5}{(6)}{ + y = 40}$ $30+y = 40$ $30{-30} + y = 40{-30}$ ${y = 10}$ You can also plug ${x = 6}$ into $\thinspace {4x-y = 14}\thinspace$ and get the same answer for $y$ : ${4}{(6)}{ - y = 14}$ ${y = 10}$